FL/HFL link invariants
A computational study of link Floer homology, F_L expansions, and the geometry of associated polytopes.
Caltech Quantum Topology Group
We study knots, 3-manifolds, and quantum invariants at the intersection of geometry, topology, and quantum field theory — with an emphasis on open computational data and reproducible research.
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Learn moreAbout our research
The Caltech Quantum Topology Group explores the rich interface between low-dimensional topology, quantum field theory, and representation theory. Our work focuses on understanding the deep connections between knot invariants, 3-manifold invariants, and their origins in physics — from Chern-Simons theory to categorification and beyond.
A central theme of our research is the use of computational experiments to discover new mathematical structures and test conjectures. We believe in open science: our datasets, code, and computational results are freely available to support both theoretical advances and emerging AI-driven approaches to mathematical discovery.
Research in the group has been supported in part by the Simons Collaboration on New Structures in Low-Dimensional Topology, the Simons Foundation, and the National Science Foundation.
Recent projects
Data & software
Open datasets and tools for working with knots, links, and 3-manifolds. Use them in your own experiments, or as benchmarks for new conjectures and models.
FL/HFL Links
Computations of link Floer homology and F_L expansions, with associated polytope data.
Gukov-Manolescu series (F_K)
This table contains the the first few terms of the Gukov-Manolescu series under the column fk_polynomial. The braid and inversion datum used to compute the inverted state sum are listed under braid and inversion_data.
Gukov-Manolescu series (F_K) for most nice Links up to 9 crossings
This table contains the first few terms (degree 9 for 2 component, degree 6 for most 3 components) of the Gukov-Manolescu series for links under the column fk_polynomial. The braid and sign diagram used to compute the invariant are listed under braid and sign_diagram.
Gukov-Manolescu series (F_K) for most nice Links of 10 crossings
This table contains the first few terms (degree 10 for 2 component, degree 6 for most 3 components) of the Gukov-Manolescu series for links under the column fk_polynomial. The braid and sign diagram used to compute the invariant are listed under braid and sign_diagram.
Normalized braids
Canonical braids up to 10 crossings, lexicographically minimal among cyclic rotations and mirror images, with each generator appearing at least twice.